Find f(x) and g(x) so that the function can be described as
y = f(g(x)).

y = (8x + 18)^8

Answer:

To solve a system of equations by graphing, you need to graph each equation on the same coordinate system and find the point where the two lines intersect. If the equations are in slope-intercept form, you can identify the slope and y-intercept and graph them. If one of the equations is in slope-intercept form, you can rewrite the other one in that form and graph them. If both equations are in other forms, you can find the x- and y-intercepts and graph them.

In this case, we have two equations:

y = x + 5

y = -2x - 1

To graph these equations, we can start by finding their intercepts:

y = x + 5

0 = x + 5

x = -5

So the intercept for y = x + 5 is (-5, 0). Similarly,

y = -2x - 1

0 = -2x - 1

x = -1/2

So the intercept for y = -2x - 1 is (-1/2, 0). Now we can plot these points on a coordinate plane and draw a line through each point. The point where these two lines intersect is our solution.

Therefore, the solution to this system of equations is (-3, 2).

Step-by-step explanation:

Answer: We can use the two given points to find the equation of the line and then plug in 39 for the calling time to find the corresponding monthly cost.

Let x be the calling time (in minutes) and y be the monthly cost (in dollars). Then we have the following two points:

(x1, y1) = (35, 16.83)

(x2, y2) = (52, 18.87)

The slope of the line passing through these two points is:

m = (y2 - y1) / (x2 - x1) = (18.87 - 16.83) / (52 - 35) = 0.27

Using point-slope form with the first point, we get:

y - y1 = m(x - x1)

y - 16.83 = 0.27(x - 35)

Simplifying, we get:

y = 0.27x + 7.74

Therefore, the monthly cost for 39 minutes of calls is:

y = 0.27(39) + 7.74 = $18.21

Step-by-step explanation:

Answer:

To find the 40th term of the sequence, we first need to identify the pattern that generates the terms. We can see that each term is obtained by adding 4 to the previous term. So the sequence is an arithmetic sequence with a common difference of 4.

Using this information, we can find the formula for the nth term of the sequence using the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

Where an is the nth term of the sequence, a1 is the first term, n is the term number, and d is a common difference.

In this case, we have a1 = 7 and d = 4. Substituting these values into the formula, we get:

an = 7 + (n - 1)4

Simplifying this expression, we get:

an = 4n + 3

Now we can use this formula to find the 40th term of the sequence:

a40 = 4(40) + 3

a40 = 160 + 3

a40 = 163

Therefore, the 40th term of the sequence is 163.

Answer:

angle

Step-by-step explanation:

since there is a < sign, that makes it an angle. I'm not sure if that is the whole problem, or if It is missing a picture. Hope this helps!

Answer: i know it is acute

The required graph of the function given; h (x) has been attached.

In mathematics, graph theory is the study of graphs, which are mathematical structures used to represent pairwise interactions between objects. In this definition, a network is made up of nodes or points called vertices that are connected by edges, also called links or lines. In contrast to directed graphs, which have edges that connect two vertices asymmetrically, undirected graphs have edges that connect two vertices symmetrically. Graphs are one of the primary areas of study in discrete mathematics.

Here as per the question the graph of the function, h (x) has been attached.

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Answer:

The circumference of the circle is 119.32 ft.

Step-by-step explanation:

The circumference of a circle can be solved through the formula:

C = πd

where d is the diameter

Given: d = 38 ft

π = 3.14

Solve:

C = πd

C = 3.14 (38 ft)

C = 119.32 ft

The limit of the expression as x approaches 1 is 5.

Explain limit

A limit is a value that a function or sequence approaches as the input or index approaches a specific value or infinity. It is used to describe the behaviour of a function or sequence as it approaches a certain point or as the input values become infinitely large or small. The limit is an essential concept in calculus and is used to solve problems involving derivatives, integrals, and infinite series.

According to the given information

Here we  use algebraic manipulation and direct substitution to find the limit:

lim x→1 [(x² + 1)/(x + 1) + x² + 3]

= lim x→1 [(x² + 1)/(x + 1)] + lim x→1 (x² + 3) (by the limit laws of algebra)

= [(1² + 1)/(1 + 1)] + (1² + 3) (by direct substitution)

= (2/2) + 4

= 1 + 4

= 5

Therefore, the limit of the expression as x approaches 1 is 5.

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The translation used to create the image A'B'C'D', from the pre-image, ABCD is; 7 units to the right

A translation transformation is one in which the location of the points on the pre-image is changes but the size, and orientation of the pre-image is preserved.

The coordinates of the vertices of the polygon ABCD are; (1, 5), (3, 1), (7, 1), (5, 5)

The coordinates of the vertices of the polygon A'B'C'D' are; (8, 5), (10, 1), (14, 1), (12, 5)

Whereby the vertices of the image and the preimage are;

A(1, 5), B(3, 1), C(7, 1), D(5, 5), and A'(8, 5), B'(10, 1), C'(14, 1), D'(12, 5), the difference in the x and y-values indicates;

A' - A = (8 - 1, 5 - 5) = (7, 0)

B' - B = (10 - 3, 1 - 1) = (7, 0)

C' - C = (14 - 7, 1 - 1) = (7, 0)

D' - D = (12 - 5, 5 - 5) = (7, 0)

Therefore, the transformation used to create the image A'B'C'D' from the pre-image, ABCD is a translation; 7 units to the right

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Answer:$26,141.13.

Step-by-step explanation:

Using the formula A = P * (1 + r/n)^(n*t), where A is the balance, P is the principal, r is the interest rate, n is the number of times per year that the interest is compounded, and t is the time in years, we can calculate the balance in the savings account after 10 years:

A = 8,063.00 * (1 + 0.1469/4)^(4*10)

A ≈ 26,141.13

Therefore, the balance in the savings account after 10 years, rounded to the nearest cent, is $26,141.13.

The approximated area of the shaded region is 92.54 square units

From the question, we have the following parameters that can be used in our computation:

The area of the shaded region in the figure is calculated as

Shaded region = Circle - Isosceles right triangle 1 - Isosceles right triangles 2

Using the given dimensions, we have

Shaded region = 3.14 * 6^2 - 1/2 * 5^2 - 1/2 * 4^2

Evaluate

Shaded region = 92.54

Hence, the shaded region is 92.54 square units

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The height of the heater is approximately 6.6 feet.

According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.

We can use the Pythagorean theorem to find the height of the pyramid. Let's call the height "h". Then, the slant height is the hypotenuse of a right triangle with base and height both equal to 10 feet, so we have:

h² + 10² = 12²

Simplifying and solving for h, we get:

h² + 100 = 144

h² = 44

h ≈ 6.6 feet

Therefore, the height of the heater is approximately 6.6 feet.

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Answer:

data given

principal 300

rate12%

time 4 years

Step-by-step explanation:

from

A=P[1+r/100]^n

where

A is amount

p is principal

r is rate

n is interest period

now,

A= 300[1+12/(100×12)]^(12×4)

A=300×1.01^48

A=483.67

: .would be 483.67

The polynomial in factor form is y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3).

In this problem we find a representation of polynomial set on Cartesian plane, whose expression is described by the following formula in factor form:

y(x) = a · (x - r₁) · (x - r₂) · (x - r₃) · (x - r₄)

Where:

Then, by direct inspection we get the following information:

y(0) = - 3, r₁ = - 3, r₂ = - 1, r₃ = 2, r₄ = 3

First, determine the lead coefficient:

- 3 = a · (0 + 3) · (0 + 1) · (0 - 2) · (0 - 3)

- 3 = a · 3 · 1 · (- 2) · (- 3)

- 3 = 18 · a  

a = - 1 / 6

Second, write the complete expression:

y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3)

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This problem involves integration and algebraic manipulation, and belongs to the subject of calculus. The solutions are:

[tex]A) $\int_{0}^{2} (f(x) + g(x)) dx = -3$[/tex]
[tex]B) $\int_{0}^{3} (f(x) - g(x)) dx = -4$[/tex]
[tex]C) $\int_{2}^{3} (3f(x) + g(x)) dx = -32$[/tex]

This is a problem that asks us to find the values of some definite integrals using given values of other definite integrals. We are given three definite integrals, and we are asked to compute three other integrals involving the same functions, using the given values.

The problem involves some algebraic manipulation and the use of the linearity of the integral.

It also involves finding the constant "a" that makes a definite integral equal to zero. The integral involves two functions, "f(x)" and "g(x)," whose definite integrals over certain intervals are also given.

See the attached for the full solution.

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Answer:

A= $116.05

Step-by-step explanation:

A=P(1+E)kt

A=100(1+0.03/2)^10

A= $116.05

The value of Tanθ is 20/21.

What is Pythagorean Theorem?

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here, we have

Given: sinθ = -20/29 and that angle terminates in quadrant III.

We have to find the value of tanθ.

Using the definition of sine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

Sinθ = Perpendicular/hypotenuse

Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.

Adjacent = - √Hypotenuse² - perpenducualr²

Replace the known values in the equation.

Adjacent = -√29² - (-20)²

Adjacent = -21

Find the value of tangent.

Tanθ = Perpendicular/base

Tanθ = -20/(-21)

Hence, the value of Tanθ is 20/21.

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1) the  expression in words can be written as "Nineteen times the difference between twenty-three thousand and seven hundred and eighty-nine."

1) The expression (23,000-789) × 19 can be written in words using the following steps:

The expression inside the parentheses is the difference between 23,000 and 789, which is 22,211.

The expression is then multiplied by 19, which means it is being increased by 19 times.

So the final expression in words can be written as "Nineteen times the difference between twenty-three thousand and seven hundred and eighty-nine."

2) The expression 2.6+(88×7) can be read in words using the following steps:

The expression inside the parentheses, 88×7, means 88 multiplied by 7.

The result of the multiplication is 616.

The expression then becomes 2.6 added to 616.

So the final expression in words can be read as "Two point six plus six hundred and sixteen."

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Answer: To find two complex numbers that add up to c = -11 + 3i, we can set up the following system of equations:

a + b = -11

ai + bi = 3i

Solving for a and b, we can multiply the first equation by i and subtract it from the second equation multiplied by -1 to eliminate b:

ai + bi = 3i

-ai - bi = 11i

0 + 10bi = 14i

Simplifying, we get b = 1.4. Substituting this into the first equation gives:

a + 1.4 = -11

a = -12.4

So the two complex numbers that add up to c are -12.4 + 1.4i and 1.4i.

To find the value of iº, we need to evaluate i raised to the power of 90 degrees (or pi/2 radians) using Euler's formula:

e^(iθ) = cos(θ) + i sin(θ)

So we have:

iº = i^(90°) = e^(iπ/2) = cos(π/2) + i sin(π/2) = 0 + i(1) = i

Therefore, iº = i.

Step-by-step explanation:

Answer:

3.14 cm^2

Step-by-step explanation:

1. Find radius:

If diameter is 2, divide it by 2 to get radius = 1

2. Find formula:

A=πr^2

3. Plug in:

A = π(1)^2

4. Solve (multiply):

A = π(1)^2:

3.14159265359

Or

3.14 cm^2

Answer:

3.14 cm^2

Step-by-step explanation:

A=[tex]\pi[/tex]r^2

r=2

2/2=1

A=[tex]\pi[/tex](1)^2

=[tex]\pi[/tex]1

≈3.14x1

≈3.14cm^2

It follows that the translation direction is 8 units to the left and 0 units up or down.

A translation is a geometric change in Euclidean geometry where each point in a figure, shape, or space is moved uniformly in one direction. A translation can either be thought of as moving the origin of the coordinate system or as adding a constant vector to each point

The new vertices of a triangle with vertex locations of (0,0), (1,0), and (0,1), for instance, would be (2,3, (3,3), and (2,4) if the triangle were translated 2 units to the right and 3 units up.

We can use the following procedures to get the translation direction and number of units for R′(7, 4):

1. Determine the difference between R and R′'s x-coordinates:  −7 − 1 = 8

2. Determine the difference between R and R′'s y coordinates: 4 − 4 = 0

It follows that the translation direction is 8 units to the left and 0 units up or down.

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Answer:

mean = 24

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

the sum of the data set is

sum = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168

there is a count of 7 in the data set , then

mean = [tex]\frac{168}{7}[/tex] = 24

1. The initial mass of the sample was 32 mg. 2. The mass of the sample 7 weeks after the start is approximately 0.162 mg.

An unstable atomic nucleus releases particles or electromagnetic radiation as it undergoes radioactive decay, changing into a different nucleus. Since this process is unpredictable and spontaneous, the decay's timing cannot be anticipated. The radioactive substance's half-life, or the amount of time it takes for half of its radioactive atoms to decay, is used to calculate the rate of decay. Radiometric dating, nuclear energy production, and medical imaging all employ radioactive decay, which can cause the emission of alpha particles, beta particles, or gamma rays. Understanding the behaviour of matter at the atomic and subatomic level requires knowledge of radioactive decay.

1. The radioactive decay is given by the formula:

[tex]N(t) = N_0 * (1/2)^{(t/T)}[/tex]

Now, for half-life of Palladium-100 is 4 days and t = 16 and N(t) = 2 we have:

[tex]2 = N_0 * (1/2)^{(16/4)}\\2 = N_0 * (1/2)^4\\2 = N_0* 1/16\\N_0 = 2 * 16\\N_0 = 32 mg[/tex]

2. Foe 7 weeks:

7 weeks = 7 * 7 days = 49 days.

[tex]N(49) = N_0 * (1/2)^{(49/4)}\\N(49) = 32 * (1/2)^{(49/4)}\\N(49) = 0.162 mg[/tex]

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3 Σ n=1 (17n-25) = 3(27) = 81.The notation "3 sigma n=1 (17n-25)" represents a mathematical series. The Greek letter sigma (Σ) indicates

what is  sigma  ?

Sigma (Σ) is a Greek letter used in mathematics to represent the sum of a sequence of terms. The lowercase sigma (σ) is often used to represent standard deviation in statistics.

In the given question,

The notation "3 sigma n=1 (17n-25)" represents a mathematical series. The Greek letter sigma (Σ) indicates that we are adding up a sequence of terms, with "n=1" indicating that we start the series with n=1, and "3" indicating that we add up three terms in total.

The expression inside the parentheses, "17n-25", represents the general term in the series. To find each term in the series, we plug in the values of n=1, n=2, and n=3 into the general term and add them up:

17(1)-25 + 17(2)-25 + 17(3)-25 = -8 + 9 + 26 = 27

Therefore, 3 sigma n=1 (17n-25) = 3(27) = 81.

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find  3 ∑ n=1 (17n-25)  and give the answer ?

The expression that represents the area of the remaining rectangular portion is given as follows:

A = -4x² + 12x + 6.

To obtain the area of a rectangle, you need to multiply its length by its width. The formula for the area of a rectangle is:

Area = Length x Width

The dimensions for the rectangle are given as follows:

Hence the area is given as follows:

A = 3(4x + 2)

A = 12x + 6.

Four squares of side length x -> area = x² are cut, hence the remaining area is given as follows:

A = -4x² + 12x + 6.

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To the nearest inch, there are 4 inches in 10.16 centimetres.

The process of translating a measurement from one unit to another is known as a units conversion. This is frequently done when comparing measurements from various sources or when working with several unit systems. In order to communicate a measurement in a different unit of the same physical amount that is more suitable or useful for a specific context, units conversion is required.

If you are speaking with someone who uses the Imperial system of units, for instance, you may need to convert from metres to feet when estimating distance. If you are working with someone who utilises the American customary system, you may need to convert from kilogrammes to pounds when measuring weight.

In order to prevent mistakes in calculations and measurements, it is crucial to be precise and accurate while converting between units. Unit conversion is a crucial component of scientific and technological activity.

Since there are 2.54 centimetres in one inch, we may multiply 4 inches by 2.54 to convert them to centimetres:

4 inches * 2.54 centimeters per inch = 10.16 centimeters

We multiply by 2.54 to convert centimetres to inches:

10.16 centimeters / 2.54 centimeters per inch = 4 inches (rounded to the nearest inch)

Therefore, rounding to the closest inch, there are 4 inches in 10.16 centimetres.

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In the Unit conversion,to the nearest inch, there are 4 inches in 10.16 centimeters.

Describe Units Conversion?

The process of translating a measurement from one unit to another is known as a units conversion. This is frequently done when comparing measurements from various sources or when working with several unit systems. In order to communicate a measurement in a different unit of the same physical amount that is more suitable or useful for a specific context, units conversion is required.

If you are speaking with someone who uses the Imperial system of units, for instance, you may need to convert from meters to feet when estimating distance. If you are working with someone who utilises the American customary system, you may need to convert from kilograms to pounds when measuring weight.

In order to prevent mistakes in calculations and measurements, it is crucial to be precise and accurate while converting between units. Unit conversion is a crucial component of scientific and technological activity.

Since there are 2.54 centimeters in one inch, we may multiply 4 inches by 2.54 to convert them to centimeters:

=> 4 inches * 2.54 centimeters per inch = 10.16 centimeters

We multiply by 2.54 to convert centimeters to inches:

=> 10.16 centimeters / 2.54 centimeters per inch

=> 4 inches (rounded to the nearest inch)

Therefore, rounding to the closest inch, there are 4 inches in 10.16 centimeters.

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The time(s) at which the population will be greater than 460,000 organisms is between 10 and 30 hours after the culture is started.

An inequality is a comparison between two numbers or expressions that are not equal to one another. Symbols like, >,,, or are used to denote it, indicating which value is more or smaller than the other or just different.

To find the time(s) at which the population will be greater than 460,000 organisms, we need to solve the inequality:

P(t) > 460,000

Substituting the given equation for P(t), we get:

-1500t² + 60,000t + 10,000 > 460,000

Simplifying this inequality, we get:

-1500t² + 60,000t - 450,000 > 0

Dividing both sides by -1500 and flipping the inequality sign, we get:

t² - 40t + 300 < 0

We can solve this inequality by factoring the quadratic equation:

(t - 10)(t - 30) < 0

The roots of this equation are t = 10 and t = 30. Plotting these values on a number line, we can see that the solution to the inequality is:

10 < t < 30

Therefore, the time(s) at which the population will be greater than 460,000 organisms is between 10 and 30 hours after the culture is started.

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